二次损失下一般的回归系数线性估计的容许性

本文研究线性模型中一般的回归系数的估计问题,用统计决策函数理论中容许性准则,讨论了线性估计的优良性,通过将一般的非可估回归系数转化成可估的情形,得到了一个线性估计在线性估计类中是容许估计的充分必要条件。     

增长曲线模型中线性估计类所有可容许估计

对增长曲线模型中回归矩阵的函数的线性估计进行了研究。在矩阵损失下 ,作者得到了线性估计在一切线性估计类中可容许的充要条件     

增长曲线模型非齐次线性估计的可容许性

本文讨论了增长曲线模型中回归矩阵的函数的估计 ,在矩阵损失下 ,作者得到了非齐次线性估计在非齐次线性估计类中可容许的充要条件。     

具有均匀协方差结构的误差方差非负二次估计的可容许性

在二次损失函数下,研究了线性模型中具有均匀协方差结构的误差方差非负二次估计的可容许性,给出了设计矩阵为1向量时,估计可容许的充要条件。     

误差方差二次型估计模型的转化

研究一般的回归模型中误差方差的二次型估计的容许性，研究方法是模型的整体转化和局部转化，结果有：（１）二次约束下的线性模型等价于相应的无约束的线性模型。（２）线性（齐次或非齐次）等式约束下的线性模型等价于某个无约束的线性模型。（３）单个非齐次不等式约束下的线性模型等价于某个无约束的线性模型。（４）通过例子证明了多个线性不等式约束的线性模型不能等价于某个无约束的线性模型。（５）某类非齐次二次型估计的容许性等价于相应的齐次二次型估计的容许性     

增长曲线模型误差方差的二次型可容许估计

对于增长曲线模型,在二次损失函数下,研究了当C为列满秩,而A为行秩亏矩阵时误差方差的二次型估计的容许性,用矩阵形式给出了二次型估计可容许的充要条件。     

两类增长曲线模型误差方差估计——二次型容许估计

研究两类增长曲线模型误差方差的二次型估计的容许性，在损失函数为（ｄ－σ２）／σ４时，对这两类模型分别给出一个二次型估计在二次型估计类中可容许的充要条件     

增长曲线模型误差方差的二次型估计可容许的必要条件

对于增长曲线模型Y=ABC εEε=0,cov(vecε)=σ2(Ip(○X)G)在二次损失函数下,研究了当A为非行满秩矩阵时误差方差的二次型估计的容许性,并得出二次型估计可容许的必要条件.     

协方差阵二次型容许估计的一个必要条件

研究协方差阵Σ的二次型容许估计问题。设 y1,y2 ,… ,yniid,n≥ 2 ,y1与 p维正态分布N (β,Σ )有相同的前四阶矩。其中β =(β1,β2 ,… ,βp)′∈ Rp与Σ =(σij) p× p >0均未知。记 y =△ (y1,y2 ,… ,yn)′。在二次损失 L (d ,Σ ) =tr(d -Σ) 2下给出Σ的二次型估计 a S2 + nby-y-′是容许估计的必要条件为 :(n - 1) a + b + 2 max(a,b)≤ 1。此必要条件比张立振等协方差阵的二次型容许估计中的必要条件有了明显的加强     

协方差阵的二次型容许估计

该文研究协方差阵 Σ的二次型容许估计问题。设 y1,y2 ,… ,yn iid,n≥ 2 ,y1与 p维正态分布 N β,Σ有相同的前四阶矩。其中 β=β1,β2 ,… ,βp ′∈ RP与 Σ=σij p× p>0均未知。记y=△ (y1,y2 ,… ,yn)′。在损失函数 L(d,Σ) =tr(d- Σ) 2下给出 Σ的二次型估计在 D={ y′ Ay∶ A≥ 0 ,A∈ Rn× n}中容许的必要条件是 y′ Ay必须具有 a S2 + nb y-y-′的形式。并进而得出当 b=0时 a S2 作为Σ的容许估计的充要条件     

A nearly unbiased inherently stable bearings-only tracker

A pseudolinear estimator for bearings only tracking is presented. It is demonstrated through calculations and simulations that it has a performance close to the computationally far more complex maximum-likelihood estimator, in contrast to the earlier well-known pseudolinear estimator in Cartesian coordinates. Using the mean time point as the time reference of this estimator is necessary in order to avoid bias     

Structure estimation accuracy in discrete layered media

We consider the problem of estimating structure (interface reflection coefficient values) from noisy reflection observations of a discrete, layered, lossless waveguide; this is a special case of the general acoustic reflection inverse problem. Our approach is to develop a statistical lower bound, the Cramer-Rao bound, on estimator performance. We demonstrate, by computing the bound for the one- and two-reflector cases, that the bound is not merely theoretical but also provides, through its parametric behavior, physical insight into the estimation problem. In addition, we present two estimator structures for this problem, a statistically optimal estimator, (maximum-likelihood), and a suboptimal estimator (based on the special character of the medium's response), and compare their performance. We perform Monte Carlo tests to verify that, for high signal-to-noise ratios, estimator performance is predicted by the Cramer-Rao bound. Moreover, we find that in these regions the ad hoc estimator performs comparably to the maximum likelihood.     

ROTARY SPECTRAL ESTIMATION AND ITS APPLIED EXAMPLES FOR OCEAN CURRENT VECTOR TIME SERIES

The mathematical background of the rotary spectral estimation of the ocean current vector and the related rotary variates are described briefly in this paper, some achievements in the confidence intervals of the rotary spectral estimator of the vector are summerized. On this basis, the expectation and variance expressions for the autospectral estimator of the rotary spectrum of vector are derived by resorting to some hypotheses and results of the scalar spectral estimator. And then its confidence interval is given. Finally, some computation examples for the rotary spectral estimator of vector are furnished.     

Adaptive State Estimation for a System With Unknown Input and Measurement Bias

An adaptive state estimator for passive underwater tracking of maneuvering targets is developed. The state estimator is designed specifically for a system containing independent unknown or randomly switching input and measurement biases. In modeling the stochastic system, it is assumed that the bias sequence dynamics for both input and measurement can be modeled by a semi-Markov process. By incorporating the semi-Markovian concept into a Bayesian estimation technique, an estimator consisting of a bank of parallel adaptively weighted Kalman filters has been developed. Despite the large and randomly varying biases, the proposed estimator provides an accurate estimate of the system states.     

广义岭估计的谱分解式和Liu型广义岭估计

首先从多参数岭估计,即广义岭参数人手,给出其谱分解形式。然后就岭估计会使估值偏差增大的问题,在Liu估计的基础上,推导出一种新的有偏估计方法——Liu型广义岭估计,并给出该方法的模型、解式。Liu型广义岭估计可以在尽量不增大偏差的同时改进病态性,获得更好的估值。最后通过算例进行了比较分析。     

A minimum variance unbiased estimator for ocean surface currentsbased on multifrequency microwave radar observations

This paper presents a minimum variance unbiased (MVU) estimator for estimating an ocean surface current using the multifrequency microwave radar technique. In this technique the current information is obtained by finding the difference between the measured phase velocities of some specific surface gravity waves and the phase velocities calculated from the dispersion relation for still water. By defining the problem as a linear estimation problem, we develop an unbiased estimator for the current component along the radar look direction, which has a variance that is inversely proportional to the sum of the squared wavenumbers of the gravity waves used in the measurements. We also study the performance of an MVU vector estimator based on radar observations along two directions. Our analysis shows that the confidence region of this estimator has the shape of an elongated ellipse with semi-axes and orientation which are dependent on the angle between the observation directions, but independent on the true current vector. Furthermore, the theoretical models are thoroughly tested using both simulated and real radar data, and these tests show very good agreement with the model predictions     

Passive sonar ML estimator for ship propeller speed

The optimal estimator in the maximum-likelihood sense fur the propeller speed of a ship, using underwater radiated cavitation noise generated by the propeller blades, is derived. From the result the number of blades on the propeller can also be derived. Results obtained for real sonar data using a digital implementation of the estimator will be presented     

A comparison of estimators for the generalised Pareto distribution

The generalised Pareto distribution (GPD) is often used to model the distribution of storm peak wave heights exceeding a high threshold, from which return values can be calculated. There are large differences in the performance of various parameter and quantile estimators for the GPD. Commonly used estimation methods such as maximum likelihood or probability weighted moments are not optimal, especially for smaller sample sizes. The performance of several estimators for the GPD is compared by the Monte Carlo simulation and the implications for estimating return values of significant wave height are discussed. Of the estimators compared, the likelihood-moment (LM) estimator has close to the lowest bias and variance over a wide range of sample sizes and GPD shape parameters. The LM estimator always exists, is simple to compute and has a low sensitivity to choice of threshold. It is recommended that the LM estimator is used for calculating return values of significant wave height when the sample size is less than 500. For sample sizes above 500 the NEW estimator of Zhang and Stephens (2009) can give accurate results for low computational cost.     

海流剖面仪信号处理系统中最小二乘改进算法的应用研究

ADCP技术是海洋测流领域的热门技术,而频谱估计方法的研究是该技术的核心。文章介绍一种最小二乘的改进算法(ELMS),利用该算法可以很好的提取出淹没在白噪声下的正弦频谱。和传统的快速傅立叶变换方法(FFT)相比,该算法极大的压缩了数据量的要求,而且在信噪比为0DB的时候,仍能够较准确的估计出信号的谱峰位置。实验结果辩明该算法具有良好的鲁棒性。     

A Passive Localization Algorithm and Its Accurancy Analysis

The problem of estimating source location from noisy measurements of range differences (RD's) is considered. A localization technique based on solving a set of linear equations is presented and its accuracy properties are analyzed. An optimal weighting matrix for the least squares estimator is derived. The analytical expressions for the variance and bias of the estimator are validated by Monte-Carlo simulation. The problem of estimating source velocity given measurements of range differences and range-rate differences is briefly considered, and a linear equation technique is derived.